1. Field of the Invention
The present invention relates to a positioning control system for positioning at least one magnetic head or similar controlled device at a designated position at high speed.
There is recently a tendency to demand, in a computer system, a transfer of large amounts of data at high speed, and therefore, an auxiliary storage device such as a magnetic disk drive or optical disk drive is also required to transfer large amounts of data at high speed to exchange data with a host device.
To meet this requirement, it is essential that a controlled device such as a magnetic head, an optical head, a print head, or the like should be positioned at a designated position at high speed and with high accuracy. Since the controlled device is driven at a high velocity and high acceleration when such a head positioning (head seek operation) is executed at high speed, the mechanical resonance phenomenon, which forces the controlled device to vibrate even after the head positioning is completed, is likely to occur. Thus, there is a demand to provide a stable control by suppressing the mechanical resonance characteristics represented by the vibration of controlled device.
2. Description of the Related Art
In general, in a magnetic disk drive or the like, data transfer speed is limited by a rotation speed of a motor which rotates a magnetic disk or the like as a recording medium. Accordingly, if it is intended to attain a substantially higher data transfer speed with the current rotation speed, first of all, it is necessary that a larger number of recording media such as magnetic disks, each having a higher density recording surface (e.g., a track pitch thereof being less than 10 .mu.m), should be contained in a magnetic disk drive or the like to increase data recording density and data storage capacity. Next, it is necessary that a plurality of controlled devices such as magnetic heads should be provided, corresponding to the respective recording media, so as to write and read data in parallel to or from the magnetic disks by moving the plurality of magnetic heads simultaneously and at high speed with one actuator.
In other words, a number of magnetic heads are mounted on one actuator via a plurality of head arms, and therefore a plurality of mechanical resonance frequencies are generated due to the respective magnetic heads and head arms. Furthermore, since the magnetic heads must be moved at high speed, it is necessary for the respective head arms to be as light in weight as possible. Therefore, various mechanical resonance modes are likely to occur, which results in the complexity of the control of mechanical resonance characteristics.
Hereinafter, to facilitate an understanding of the mechanical resonances of controlled devices, the construction of magnetic disk drives including magnetic heads will be described representatively with reference to the drawings.
FIGS. 1(A) and 1(B) are diagrams showing a magnetic disk drive. To be more specific, FIG. 1(A) is a schematic plan view of the magnetic disk drive, and FIG. 1(B) is a schematic side view thereof. The reference numeral 50 denotes a plurality of magnetic disks, 51 a rotatable shaft, 52 an actuator, 53 arms, 54 gimbals, 55 core sliders including magnetic heads, and 56 a rotatable shaft. The rotatable shaft 51 having the magnetic disks 50 fixed thereon is rotated by an motor (not shown). In the illustrated example, ten magnetic disks 50 are fixed on the rotatable shaft 51. However, it may be also possible to a different number of magnetic disks 50 on the rotatable shaft 51 according to the required storage capacity and data transfer speed.
Further, in this example, the core slider 55 is supported on each arm 53 through two gimbals 54. The core sliders 55 move radially across the magnetic disks 50 by rotating the arms 53 about the rotatable shaft 56 of the actuator 52, and thereby each of the magnetic heads is positioned at the designated position (track). Through the magnetic heads, data are written on the magnetic disks 50 or data stored on the magnetic disks 50 are read therefrom.
As the recording density (track density) of the magnetic disks 50 increases, it is necessary to drive the actuator 52 at high speed, and to move and position the respective magnetic heads to the designated tracks at high speed and with high accuracy. In this case, the arms 53 including the core sliders 55 are driven at a high velocity and high acceleration by the actuator 52, and accordingly the mechanical resonance, which results in the vibration of the magnetic heads, becomes a problem. Thus, it is required to suppress the mechanical resonance characteristic or to transfer the resonance frequency to a higher frequency band so as to eliminate the influence on a control frequency band of the magnetic heads.
FIG. 2 is a graph showing the exemplary transfer characteristics (x/i characteristics; a response x in a head position relative to a current i supplied to a voice coil motor constituting the actuator) of the actuator. In FIG. 2, the response x is typically represented by a frequency response of a gain and phase of a head positioning control system. To be more specific, a horizontal axis represents frequency (Hz), the left vertical axis represents gain (dB), and the right vertical axis represents phase (deg). The curve (a) represents the gain characteristics, while the curve (b) represents the phase characteristics. As apparent from these transfer characteristics, there are several mechanical resonances where the gains remarkably increase, resulting from the structure of the actuator, the magnetic heads, etc. The typical resonances include a main resonance and a torsional resonance of the whole actuator, a resonance of vertical direction and a torsional resonance of the fork-shaped arms having a number of heads mounted thereon, a resonance of spring arms between the heads and the actuator, and a resonance of the voice coil motor.
The aforementioned resonance characteristics are not uniform in terms of the resonance frequency and the resonance strength of each of the storage devices, and vary depending on the storage devices. Further, even in a specific device, the resonance characteristics vary according to the temperature change, aging, and rotational position of each of the arms (head positions). In the case of controlling this type of actuator, a transfer function of the actuator F(s) and a transfer function Freso(s) representing the mechanical resonance characteristics are expressed as follows. ##EQU1## If this actuator is modeled on the assumption that it is a rigid body, it can be assumed that Freso(s)=1. Further, Km in the equation (3) is expressed assuming that a moment of inertia of the rotary type actuator is J (kg.multidot.m.sup.2), a torque constant of the voice coil motor is K.sub.T (N-m/A), and the distance between the center of rotation and the head is R.sub.H (m).
The control system for the conventional actuator having the above resonance characteristic is shown in FIG. 3. In this figure, the reference numeral 61 denotes an adder (also represented by .SIGMA.), 62 a loop compensator, 63 a notch filter group that will be described in relation to FIGS. 4 and 5, 64 a power amplifier, and 65 a controlled device (plant) including the actuator and the magnetic head. The position information of the controlled device 65 and the designated position information are given to the adder 61, and the controlled device 65 is controlled through the loop compensator 62, the notch filter group 63, and the power amplifier 64, so that the difference between the position information and the designated position information becomes a specified value such as zero.
The loop compensator 62 in this control system includes a combination of a lead lag filter adjusting a phase angle of the system for stabilizing the loop and a secondary filter for reducing noise in a high frequency band. The transfer function Gc(s) thereof representing a ratio of output signal to input signal is expressed as follows, in equation (4). ##EQU2## where Gco is a direct current gain, .omega..sub.Ld is a lead compensating angular frequency (an angular frequency corresponds to a phase angle), .omega..sub.Lg is a lag compensating angular frequency, .zeta..sub.c and .omega..sub.c are a damping ratio and a cut-off angular frequency of the secondary filter, respectively.
Generally, the loop compensator has an integrator {transfer function=[(s+.omega..sub.i)/s]} connected in series so as to eliminate a steady position error. However, in this example, the integrator is not illustrated for the sake of simplification. In the case where the controlled device 65 has no or negligible mechanical resonance characteristics, the control can be executed stably by providing the loop compensator 62 as shown in FIG. 3.
Further, it is also possible to use a state feedback regulator using the loop compensator 62 as an observer. A state equation and an output equation in this case are as expressed in the following equations (5) and (6). Based on these equations (5) and (6), an observer equation expressed in equation (7) is obtained. ##EQU3## If L1, L2 in the equation (7) are selected with reference to a related reference (G. F. Franklin, J. D. Powell and M. L. Workman "Digital Control of Dynamic Systems", Second Edition, Addison-Wesley, 1990), Estx and Estv are selected so that they become estimated values of the position x and the speed v, respectively. Accordingly, the controlled device can be controlled by selecting the gains k.sub.1, k.sub.2 in accordance with a controller equation expressed by the equation (8) using the state feedback.
However, in the case where the mechanical resonance characteristics are not negligible, a required number m of notch filters are connected in series with the loop compensator 62 in order to cancel a resonance energy caused by the large mechanical resonance characteristics, as shown in the following equation (9). In other words, the notch filter group 63 constituted by the plurality of notch filters is provided. ##EQU4## where .zeta..sub.nj denotes a damping ratio of the notch filters, .omega..sub.nj denotes a notch center angular frequency in the center of each notch portion, and d.sub.nj denotes the depth of each notch portion. Here, it is assumed that d.sub.nj &lt;1.
Further, to enable the function of the notch filter group in FIG. 3 to be understood more clearly, exemplary transfer characteristics of a single notch filter and notch filter group are illustrated in FIG. 4 and FIG. 5, respectively.
As apparent from FIG. 4, frequency characteristics of the gain of the notch filter have a notch-shaped form, where only the gain corresponding to an extremely narrow frequency range in the closest vicinity of a notch center frequency f.sub.0 is remarkably low. Through the notch filter, the input signal having the frequency f.sub.0 is eliminated and therefore substantially not transferred.
By virtue of such characteristics of the notch filter, the mechanical resonance energy generated in the resonance frequency f.sub.0 can be eliminated. Accordingly, if a plurality of notch filters are designed in conformity with the respectively corresponding resonance frequencies shown in FIGS. 2 and 5 (in FIG. 5, six resonance frequencies f.sub.0 .about.f.sub.5 are illustrated representatively), and if the notch filter group is constituted by connecting these notch filters in cascade, many mechanical resonances can be eliminated simultaneously.
In such a construction, the notch filters are each constructed so that the notch center angular frequency .omega..sub.nj coincides with the respective mechanical frequencies in the mechanical resonance characteristics. However, if the resonance frequency and the resonance strength differ depending upon the storage devices such as magnetic disk drives, it is required to design the notch filter according to the resonance frequency and the resonance strength of each storage device. Further, even in a specific device, due to the temperature change and the aging, the resonance frequency is shifted from the notch center frequency, thereby resulting in the disadvantage that the resonance characteristics cannot be suppressed effectively. If there are more mechanical resonance points of the controlled device 65, this results in a large construction of the notch filter group 63 including the notch filters corresponding to the respective resonance points (frequencies). When the notch filters are constituted by analog circuits, the number of parts is increased thereby making the notch filter group larger in size and more costly. On the other hand, when the notch filters are constituted by digital circuits, a disadvantage occurs in that provision of an expensive high speed operating DSP (digital signal processor) is necessitated, in order to process various signals at high speed so that a filter calculation time does not become longer.
Especially, in regard to the magnetic disk drive, there is a recent requirement for transferring large amounts of data at high speed as described before.
To address this requirement, the track density of each magnetic disk is designed to be as high as possible, and the number of magnetic disks contained in one magnetic disk drive is intended to be as large as possible. Further, as the number of magnetic disks increases, the number of the corresponding magnetic heads and head arms is likely to increase. Therefore, a larger number of head and head arms are fixed to one actuator, which leads to complexity of the structure of actuator. Further, since the actuator, the arms, etc., must be moved at high speed to ensure the data transfer at high speed, they are required to be fabricated, utilizing a light metal such as aluminum. Accordingly, the mechanical resonance modes and the resonance frequencies are likely to increase. Due to various resonance energies caused by such resonance modes, residual vibrations of the magnetic heads after a seek operation is completed are likely to occur over a wider frequency range.
Consequently, it becomes difficult for all these resonant energies to be canceled by only the notch filter group, in the magnetic disk drive.